Linear-motion stage

ABSTRACT

A linear-motion stage that is angularly or radially symmetric or asymmetric, or monolithic may be used as the moving mechanism in a Fourier transform spectrometer. In embodiments, a linear-motion stage includes a base; a first multiple-arm linkage extending from the base to a first carriage attachment piece; and a second multiple-arm linkage extending from the first carriage attachment piece to the base. The first multiple-arm linkage constrains a motion of the first carriage attachment piece to motion in a first plane and the second multiple-arm linkage constrains the first carriage attachment piece to motion in a second plane, the first and second planes intersecting at a plane intersection line. The first and second multiple-arm linkages constrain the motion of the first carriage attachment piece along a carriage motion line.

TECHNICAL FIELD

The present disclosure relates to a linear-motion stage.

BACKGROUND I. Linear-Motion Stages

A linear-motion stage is part of a motion system designed to restrictmotion of an object along a linear path. A linear stage usually includesa platform and a base, wherein the platform movement is restricted,relative to the base, along a line. A linear stage may be used inmanufacturing equipment or machines including robots, machine tools,assembly, semiconductor equipment, laser equipment, electronicmanufacturing equipment, atomic force microscopy (AFM), micro electricalmechanical devices (MEMS), pick and place systems, scanning devices,biomedical devices, or other industrial automation applications. Alinear stage may also be used in a variety of optical applications,including a microscopic stage, an optic lab stage, an optical fiberalignment system, an optical stage, or as an interferometer mirrortranslation stage in a Fourier transform spectrometer.

II. The Interferometer

A Fourier transform spectrometer usually includes a Michelsoninterferometer. A Michelson interferometer has a light source, adetector, a beam splitter, and two mirrors or reflectors, with one ofthe mirrors configured to move along a linear path. FIG. 1A illustratesa Michelson interferometer 50 with a planar moving mirror. The mirrorsin a Michelson interferometer 50 may be planar mirrors or corner cubereflectors. FIG. 1B illustrates a corner-cube reflector 60. Acorner-cube reflector 60 has mutually perpendicular intersecting flatsurfaces, which reflect radiation directly back towards the source,parallel to the incoming beam.

As illustrated in FIG. 1A, radiation from a radiation source strikes abeamsplitter and directs the radiation path towards two mirrors. Theradiation or radiation source is usually an ultra-violet (“UV”),visible, or infrared (IR) light source. The radiation reflects off thetwo mirrors and recombines at the beamsplitter before being redirectedtowards a detector.

The interferometer creates an optical path difference between tworadiation paths or beams by moving or translating the moving mirroralong a translational, linear path. When recombined at the beamsplitter,beams reflecting from the fixed and moving reflecting surfaces combinewith constructive or destructive interference depending on thedifference in distance of the two optical paths. The recombined beamproduces an interferogram, or a plot of light intensity as a function ofoptical path difference. The interferogram is a measurement of thecombined beams' intensity as a function of time or the movement of themoving reflecting surface. A Fourier transform may be used to transformthe interferogram's signal in the time domain to a frequency domain orspectrum.

III. Straight-Line Movement in an Interferometer

A. Motion Constraints and Degrees of Freedom

The Michelson interferometer described above requires a translationalmechanism or carriage to transport the moving mirror along atranslational, linear path. The intent of a translational mechanism orcarriage in a Michelson interferometer is to control the direction andextent the moving mirror may travel. Directions in which a translationalmechanism can move are theoretically defined by the Cartesian coordinatesystem as three X, Y, and Z vectors in which a mechanism can translateor rotate. FIG. 2A illustrates an example Cartesian coordinate system.The motions illustrated in FIG. 2A constitute a total of six Degrees ofFreedom (DOF). A mechanism may control an object's direction of motionby constraining or limiting the DOF to which it can move. For example, athree-DOF mechanism may be free to move in two translation DOF (X, Z)and one rotation DOF (Y), which defines planar motion in an X-Z plane.In another example, a one-DOF linear mechanism constrains motion to aline. FIG. 2B illustrates motion constrained to a line. The line may bealong the Y-axis shown in FIG. 2A.

Over-constrained mechanisms are usually unable to move, or not able tomove well, in any direction or in any of the six DOF unless themechanism is designed, manufactured, or aligned so that overconstraining components substantially allow motion in the intendeddirection. Another solution for over constraint is to increase themechanism's compliance, or allowing the mechanism to move in directionsother than the mechanism's intended direction of motion such that thecompliance alleviates the over constraint. FIG. 2C illustratesover-constrained linear motion: a first translational component mayconstrain motion within a first plane, a second translational componentmay constrain motion within a second plane, and a third translationalcomponent may constrain motion within a third plane. If the first,second, and third planes are not parallel to a common line, do notintersect along a common line, or if the intersection of the third planeis not parallel to a line formed by the intersection of the first twoplanes, as illustrated in FIG. 2C, the total allowable motion may beover-constrained.

B. The Porch Swing

The “porch swing” carriage has been used for moving or translating themoveable mirror in an interferometer. FIGS. 3A and 3B illustrate a porchswing with a planar reflecting surface and a corner cube reflector,respectively. The corner cube in FIG. 3B illustrates a corner cubereflector as a right-angle reflecting surface. In both FIGS. 3A and 3B,the reflecting surface moves between a “Left”, “Center”, and “Right”position, e.g., the mirror displacement, to create the optical pathdifference. In FIGS. 3A and 3B, the solid lines illustrate thereflecting surface and the solid-arrow lines illustrate radiation pathswith the reflecting surface in the center position. The dashed lines anddashed-arrow lines in FIGS. 3A and 3B illustrate the reflecting surfaceand radiation paths with the reflecting surface in the right and leftpositions.

FIG. 3A illustrates that for a flat mirror, as the reflecting surfacemoves between the mirror displacement positions, the tilt of the flatmirror can cause a corresponding tilt or angular deviation of thereflected beam. FIG. 3B illustrates that for a corner-cube mirror, asthe reflecting surface moves laterally between the mirror displacementpositions, the reflecting surface moves up and down (e.g., lateraldisplacement or shear movement vertically, as illustrated) due to thefixed distance between the connection point on the reflecting surfaceand the top of the swing. The vertical displacement of the corner-cubemirror between mirror lateral positions can cause a shear or verticaldisplacement of the reflected beam. Angular deviation or sheardisplacement of the reflected beam can degrade an interferometer'sperformance.

SUMMARY

The inventors of the present disclosure have identified the need for alinear-motion stage with very low tilt and shear that may be used in anyhigh-precision linear motion application, including an interferometer.The present disclosure in aspects and embodiments addresses this needand problem by providing, for example, linear-motion stages that areradially symmetric or asymmetric, angularly symmetric or asymmetric, andmonolithic or an assembly of parts. The linear motion stages may besuitable for applications requiring high-performance true linear motion.For example, linear motion stages described in the present disclosuremay be used as a linear stage in manufacturing equipment or machinesincluding robots, machine tools, assembly, semiconductor equipment,laser equipment, electronic manufacturing equipment, atomic forcemicroscopy (AFM), micro electrical mechanical devices (MEMS), pick andplace systems, scanning devices, biomedical devices, or other industrialautomation applications.

The linear motion stages may also be used to move a corner-cubereflector or planar mirror in a Fourier transform spectrometer. A linearmotion stage's design may be such that the corner cube's reflected beamdirection and location remains nearly unchanged as a function of themirror displacement. An important benefit of the design is that it mayreduce or eliminate the need for stage alignment, which greatlysimplifies its implementation and cost. Embodiments of linear motionstages of the present disclosure may also have little or no stiction orhysteresis issues.

In embodiments, a linear-motion stage comprises a base; a firstmultiple-arm linkage extending from the base to a first carriageattachment piece; a second multiple-arm linkage extending from the firstcarriage attachment piece to the base. In this embodiment, the firstmultiple-arm linkage constrains a motion of the first carriageattachment piece to motion in a first plane and the second multiple-armlinkage constrains the first carriage attachment piece to motion in asecond plane. Also, the first and second planes intersect at a planeintersection line and the first and second multiple-arm linkagesconstrain the motion of the first carriage attachment piece along acarriage motion line, the carriage motion line being parallel to theplane intersection line. Also, the first and second multiple-armlinkages are arranged angularly asymmetric with respect to a planetransverse to the plane intersection line.

In a further aspect of the present disclosure, the first and secondmultiple-arm linkages are arranged radially asymmetric about thecarriage motion line. In another embodiment, the first carriageattachment piece is fully balanced such that a center of gravity of thefirst carriage attachment piece is located in a balancing plane formedby a first flexure extending from the first multiple-arm linkage to thefirst carriage piece and a second flexure extending from the firstcarriage piece to the second multiple-arm linkage.

In another linear motion stage, the first multiple-arm linkage and thesecond multiple-arm linkage attach to the carriage attachment piece atan attachment plane, the attachment plane being orthogonal to the planeintersection line. At least a portion of one of the first or secondmultiple-arm linkages may be homogeneously formed of a single material,having a joint-free continuity of the single material from a firstflexure to a rigid element. Additionally, the rigid element may have arigid-element section moduli and the flexure may have a flexure-sectionmoduli, the rigid-element section moduli being orders of magnitudegreater than the flexure-section moduli.

In another embodiment, a linear motion stage includes a thirdmultiple-arm linkage extending from the base to a second carriageattachment piece. In another embodiment, a linear motion stage includesa carriage extending from the first carriage attachment piece to thesecond carriage attachment piece along the carriage motion line.

In another aspect of the present disclosure, the linear-motion stagefurther comprises a third multiple-arm linkage extending from the baseto a second carriage attachment piece. Additionally, the thirdmultiple-arm linkage may constrain a motion of the carriage to motion inthe second plane. Also, the linear-motion stage may comprise a carriageextending from the first carriage attachment piece to the secondcarriage attachment piece along the carriage motion line. In anotherembodiment, the third multiple-arm linkage constrains a motion of thecarriage to motion in a third plane; the third plane is non-parallel tothe first and second plane; and the third plane is parallel to the planeintersection line. Additionally, the third multiple-arm linkagecomprises three, third multiple-arm linkage flexures, the three, thirdmultiple-arm linkage flexures may form three corresponding thirdmultiple-arm linkage rotation axes that are substantially parallel toeach other.

Each of the first, second, and third multiple-arm linkages mays comprisea set of three flexures and two rigid elements, wherein each set of thethree flexures and two rigid elements are connected in series. Inanother embodiment, the rigid elements have a rigid-element sectionmoduli and the flexures have a flexure-section moduli, the rigid-elementsection moduli being orders of magnitude greater than theflexure-section moduli.

A linear-motion stage may further comprise a fourth multiple-arm linkageextending from the second carriage attachment piece to the base, whereinthe fourth multiple-arm linkage constrains the motion of the carriage tomotion in the first plane. In another embodiment, the first multiple-armlinkage attaches to the carriage attachment piece at a first attachmentplane; the second multiple-arm linkage attaches to the carriageattachment piece at a second attachment plane; the third multiple-armlinkage attaches to the carriage attachment piece at a third attachmentplane; and the fourth multiple-arm linkage attaches to the carriageattachment piece at a fourth attachment plane.

In another embodiment, a linear-motion stage comprises a base; first,second, and third multiple-arm linkages extending from the base to twoends of a carriage. In this embodiment, the first, second, and thirdmultiple-arm linkages constrain motion to first, second, and thirdmotion-constrained planes. Additionally, the first, second, and thirdmotion-constrained planes may be parallel to a common line, the commonline being parallel to carriage motion line. Also, the first, second,and third multiple-arm linkages constrain the motion of the carriagealong a carriage motion line, the carriage motion line being parallel tothe plane intersection line.

In another embodiment, the first, second, and third multiple-armlinkages are arranged radially symmetric around the carriage motionline. A linear-motion stage may further comprise a fourth multiple-armlinkage extending from the base to the two ends of the carriage. In thisembodiment, the first, second, third, and fourth multiple-arm linkagesmay be arranged radially symmetric around the carriage motion line.

In other aspects of the present disclosure, at least a portion of one ofthe first or second multiple-arm linkages is homogeneously formed of asingle material, having a joint-free continuity of the single materialfrom a first flexure to a rigid element.

A linear motion stage may include a base; a first carriage end and acarriage extending from the first carriage end to a second carriage end;and first, second, and third multiple arm linkage sets. In thisembodiment, the first multiple arm linkage set comprises a first flexureextending from the base to a first rigid element; a second flexureextending from the first rigid element to a second rigid element; and athird flexure extending from the second rigid element to the firstcarriage end. Additionally, the second multiple-arm linkage comprises afourth flexure extending from the first carriage end to a third rigidelement; a fifth flexure extending from the third rigid element to afourth rigid element; and a sixth flexure extending from the fourthrigid element to the base. Also, the third multiple-arm linkagecomprises a seventh flexure extending from the base to a fifth rigidelement; an eighth flexure extending from the fifth rigid element to asixth rigid element; and a ninth flexure extending from a sixth rigidelement to the second carriage end. Additionally, the first, second, andthird flexures form corresponding first, second, and third rotation axesthat are substantially parallel to each other. Similarly, the fourth,fifth, and sixth flexures form a corresponding fourth, fifth, and sixthaxis that are substantially parallel to each other and substantiallyorthogonal to the first, second, and third axis. Finally, the seventh,eighth, and ninth flexures form a corresponding seventh, eighth, andninth axis that are substantially parallel to each other and the fourth,fifth, and sixth axes.

In a further aspect of the present disclosure, a linear-motion stagecomprises a base; first, second, and third multiple-arm linkagesextending from the base to two ends of a carriage. In this embodiment,the first, second, and third multiple-arm linkages constrain motion tofirst, second, and third motion-constrained planes, the first, second,and third motion constrained planes intersecting at a plane intersectionline. Also, the first, second, and third multiple-arm linkages constrainthe motion of the carriage along a carriage motion line, the carriagemotion line being parallel to the plane intersection line. Additionally,at least portion of one of the first, second, or third multiple-armlinkages is homogeneously formed of a single material, having ajoint-free continuity of the single material from a flexure to a rigidelement.

Additionally, the first, second, and third multiple-arm linkages may bearranged radially symmetric around the carriage motion line. Also, alinear motion stage may include a fourth multiple-arm linkage extendingfrom the base to the two ends of the carriage. In another embodiment,the first, second, third, and fourth multiple-arm linkages are arrangedradially symmetric around the carriage motion line.

In another embodiment, the first, second, and third multiple-armlinkages each comprise a first blade flexure extending from the base torespective first, second, and third rigid elements and the first,second, and third multiple-arm linkages each comprise a second bladeflexure extending from their respective first, second, and third rigidelement to the base.

In another embodiment, a method for moving a device comprises moving thedevice along a linear path using the linear-motion stage of any of theembodiments described above.

Features from any of the above-mentioned embodiments may be used incombination with one another in accordance with the general principlesdescribed herein. These and other embodiments, features, and advantageswill be more fully understood upon reading the following detaileddescription in conjunction with the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate a number of exemplary embodimentsand are part of the specification. Together with the followingdescription, these drawings demonstrate and explain various principlesof the instant disclosure.

FIG. 1A illustrates the motion of a Michelson interferometer.

FIG. 1B illustrates a corner cube reflector.

FIG. 2A illustrates an example Cartesian coordinate system.

FIG. 2B illustrates motion constrained to a line.

FIG. 2C illustrates over-constrained linear motion.

FIG. 3A illustrates a porch swing carriage with a planar mirror.

FIG. 3B illustrates a porch swing carriage with a corner cube reflector.

FIG. 4A illustrates a traditional Sarrus linkage.

FIG. 4B illustrates the motion of one double-arm linkage of a Sarruslinkage.

FIG. 4C illustrates the motion of both double-arm linkages in atraditional Sarrus linkage.

FIGS. 5A-5D illustrate various flexures.

FIG. 6A illustrates motion of a flexure.

FIG. 6B illustrates rotational motion of a flexure.

FIG. 6C illustrates rectilinear motion of a flexure.

FIG. 6D illustrates motion of another flexure.

FIGS. 6E and 6F illustrate plan and isometric views of twofine-positioning linear stages.

FIG. 7A illustrates the motion of one double-arm linkage that isangularly asymmetrical.

FIG. 7B illustrates two double-arm linkages that are angularly andradially asymmetrical—the double-arm linkages are orthogonal to eachother.

FIG. 7C illustrates an end view of two double-arm linkages that areangularly and radially asymmetrical—the double-arm linkages arenon-parallel to each other.

FIG. 8A illustrates an end view of an angularly and radially symmetricalthree-arm linear-motion stage.

FIG. 8B illustrates a side view of the linear-motion stage in 8A.

FIG. 8C illustrates an isometric view of the linear-motion stage in 8Aand 8B.

FIG. 9A illustrates an end view of an example angularly and radiallysymmetrical four-arm linear-motion stage.

FIG. 9B illustrates a side view of the linear-motion stage in 9A.

FIG. 9C illustrates an isometric view of the linear-motion stage in 9Aand 9B.

FIG. 10A illustrates an example angularly and radially asymmetricallinear-motion stage with four multiple-arm linkages.

FIG. 10B illustrates an elevation view of an example multiple-armlinkage used in the linear-motion stage of FIG. 10A.

FIGS. 11A-11E illustrate elevation views of various example multiple-armlinkages.

FIG. 12A illustrates an example angularly and radially asymmetricallinear-motion stage with two multiple-arm linkages.

FIG. 12B illustrates another example angularly and radially asymmetricallinear-motion stage with two multiple-arm linkages attached to thecarriage end at two different planes orthogonal to the carriage motionline.

FIG. 13 illustrates an example angularly and radially asymmetricallinear-motion stage with two multiple-arm linkages and a carriage.

FIG. 14 illustrates an example angularly and radially asymmetricallinear-motion stage with three multiple-arm linkages and a carriage.

FIG. 15A illustrates an example angularly and radially asymmetricallinear-motion stage with four multiple-arm linkages and a carriage.

FIG. 15B illustrates another example angularly and radially asymmetricallinear-motion stage with four multiple-arm linkages attached to two endsof a carriage at four different planes orthogonal to the carriage motionline.

FIGS. 16A-16C illustrate top, elevation, and side views, respectively ofthe linear-motion stage of FIG. 15A.

FIGS. 17A-17B illustrate top and elevations views of the linear-motionstage of FIG. 15A in motion.

FIG. 18A illustrates an isometric view of an example, angularly andradially symmetrical, three-arm linear-motion stage.

FIG. 18B illustrates a side view of the linear-motion stage in 18A.

FIG. 19A illustrates an isometric view of another angularly and radiallysymmetrical, three-arm linear-motion stage.

FIG. 19B. illustrates an isometric view of another angularly andradially symmetrical, three-arm linear-motion stage.

FIG. 19C illustrates a side view of the linear-motion stage in 19A.

FIG. 20A illustrates an isometric view of an example, angularly andradially symmetrical, four-arm linear-motion stage.

FIG. 20B illustrates a side view of the linear-motion stage in 20A.

FIG. 21A illustrates an isometric view of another angularly and radiallysymmetrical, four-arm linear-motion stage.

FIG. 21B illustrates a side view of the linear-motion stage in 21A.

While the embodiments described herein are susceptible to variousmodifications and alternative forms, specific embodiments have beenshown by way of example in the drawings and will be describe in detailherein. However, the exemplary embodiments described herein are notintended to be limited to the particular forms disclosed. Rather, thisdisclosure covers all modifications, equivalents, and alternativesfalling within the scope of the appended claims.

DETAILED DESCRIPTION

The present disclosure covers apparatuses and associated methods for amultiple arm linkage linear carriage that may be used as a linear-motionstage. In the following description, numerous specific details areprovided for a thorough understanding of specific preferred embodiments.However, those skilled in the art will recognize that embodiments can bepracticed without one or more of the specific details, or with othermethods, components, materials, etc. In some cases, well-knownstructures, materials, or operations are not shown or described indetail in order to avoid obscuring aspects of the preferred embodiments.Furthermore, the described features, structures, or characteristics maybe combined in any suitable manner in a variety of alternativeembodiments. Thus, the following more detailed description of theembodiments of the present invention, as illustrated in some aspects inthe drawings, is not intended to limit the scope of the invention, butis merely representative of the various embodiments of the invention.

In this specification and the claims that follow, singular forms such as“a,” “an,” and “the” include plural forms unless the content clearlydictates otherwise. All ranges disclosed herein include, unlessspecifically indicated, all endpoints and intermediate values. Inaddition, “optional”, “optionally”, or “or” refer, for example, toinstances in which subsequently described circumstance may or may notoccur, and include instances in which the circumstance occurs andinstances in which the circumstance does not occur. The terms “one ormore” and “at least one” refer, for example, to instances in which oneof the subsequently described circumstances occurs, and to instances inwhich more than one of the subsequently described circumstances occurs.

IV. The Sarrus Linkage

The Sarrus linkage may be used for moving or translating a carriage in alinear-motion stage. The Sarrus linkage is a mechanism that controlsmotion to a line. FIG. 4A illustrates a Sarrus linkage with a lowerhorizontal plate, an upper horizontal plate, and two double-arm linkageswith their respective hinges.

Linkage configurations, or the geometry of linkage configurations, arereferred to in this disclosure as “symmetrical” and “asymmetrical.”Symmetry is the correspondence of size, angle, or arrangement of partson opposite sides of a plane. There are at least two types of geometricsymmetry or asymmetry related to linkage configurations. A first type isradial symmetry, or the radial spacing of linkage arms around an axis orline of motion. A second type is angular symmetry, or how the angles ofeach link of a double-arm linkage are symmetric about a plane transverseto the travel direction through the linkage set's entire range ofmotion. For example, FIGS. 4A and 4B illustrate a Sarrus linkage that isradially asymmetric but angularly symmetric.

The Sarrus linkage is traditionally constructed of two double-armlinkages with equal length-arms, i.e., angularly symmetric. A Sarruslinkage also has linkages radially spaced 90-degrees about the directionof motion (the Z-axis in FIG. 4A), i.e., radially asymmetric. Eachdouble-arm linkage defines a 3-DOF planar motion in which the free endcan move. For example, one double-arm linkage constrains motion of theupper horizontal plate (relative to the lower-horizontal plate) tomotion in the X-Z plane and Y-rotation. The other double-arm linkageconstrains motion of the upper horizontal plate (again relative to thelower-horizontal plate) to motion in the Y-Z plane and X rotation.Because the two linkage sets are radially spaced at 90-degrees relativeto each other, i.e., radially asymmetric, their different planes ofmotion intersect along the Z-axis. This intersection line constrains thefree-end motion of each link to linear movement along the Z-axis.

FIG. 4B illustrates the motion of one double-arm linkage of a Sarruslinkage. FIG. 4C illustrates in an isometric view the motion of bothdouble-arm linkages in a Sarrus linkage. The fixed end of each linkageis illustrated with a filled-in circle or dot and the moving end isillustrated as a cross, shown in three different positions. The dashedlines illustrate the different positions of the double-arm linkages.

The design of the traditional Sarrus linkage is such that when adouble-arm is at the fully extended, extreme end of travel, its twolinks, or arms, are parallel to each other. Both FIGS. 4A and 4Billustrate that in a typical Sarrus linkage configuration, each rigidelement or link of each double-arm is the same length. Additionally, theangles formed between each link of a double-arm to a plane transverse tothe travel direction are equal through the entire range of motion, e.g.angularly symmetric. For example, in FIG. 4B, the “First Angle” is theangle formed between the first rigid link and the plane transverse tothe travel direction. Similarly, the “Second Angle” is the angle formedbetween the second rigid link and the plane transverse to the traveldirection. In a traditional Sarrus linkage, the First and Second Anglesare equal to each other throughout the range of travel. This is alsotrue in the Sarrus linkage illustrated in FIG. 4A: the angles formedbetween the rigid links and the plane transverse to the travel directionare equal throughout the linkages' range of motion.

A. Linkages, Flexures, and Means for Moving a Sarrus Linkage

1. Linkages

One method of moving a Sarrus linkage through its range of motion isthrough linkages. Linkages are used in industrial machinery to transfermovement from one component to another. A linkage is commonly anassembly of parts made of rigid links joined together at onedegree-of-freedom pivot points. A pivot point joins rigid links usingbearings, bushings, or flexures. Current linkage applications includethe reciprocating gasoline engine, car suspensions, pumps, bottleopeners, etc.

2. Flexures

Flexures deflect and deform within the elastic region of the material ofwhich the flexure is made. In embodiments, a flexure may be simply oneor more metal pieces with a thin cross-section as compared to attachedrigid members. Typically, a flexure is made of metal, and flexures maybe formed to be of a suitable dimension such that they operate at alltimes within the elastic deformation region, as opposed to plasticdeformation, of the metal in which they are formed.

Flexures are components with a thin flexible region that joins rigidelements together. The thin region is allowed to flex or bend to achievemotion. FIGS. 5A-5D illustrate various flexures. Typically, increasingthe flexible region of a flexure increases its range of motion anddecreases it movement accuracy. Said differently, a flexure's ability toaccurately move is inversely proportional to the extent it can move.Flexures either rigidly connect to, or are monolithically integral to,rigid elements. Flexures are not typically designed to stretch orcompress as coil springs do. To the inventors' knowledge, no one hasbuilt or taught a Sarrus linkage with flexures, or monolithicallyconstructed with flexures.

Flexures resist motion between the rigid elements that react against thewide or stiff cross sectional direction and allow movement when a forcereacts against the flexures thin or weak direction. Flexures commonlydefine a relative pivot axis about which the flexure bends. Beamflexures, like the ones illustrated in FIGS. 5A and 5B, are thin,plate-like springs, which, depending on the mounting orientation, caneither rotate or translate.

A flexure may be machined from the same material as its attached rigidmember or may be a separate piece attached to the rigid elements. Inembodiments, flexures and rigid elements may be manufactured or formedfrom a single, monolithic, integral, or homogeneous piece of material.Typically, that material will be a metal. Aluminum, steels, and othermore exotic metals may serve this function.

In contrast to flexures, a rigid element or member is a comparativelyrigid segment. For an individual flexure or rigid element, by rigid ismeant that the rigid members' section modulus in each dimension issubstantially greater than the minimum section modulus of a flexure thatis designed to flex. In embodiments, the section modulus of a rigidelement may be orders of magnitude larger than the section moduli offlexures about their bending axes. For example, a flexure that isdesigned or required to flex, e.g., allow its attached rigid members tomove, rotate, or pivot relative to each other about the flexural joint,may need to be flexible (not rigid), and may have a section modulusorders of magnitude less than the section moduli of its attached rigidmembers. The less motion a flexure must bend or flex, the more rigid itcan be, or the more similar its section modulus can be to a rigidelement.

3. Types of Flexure Motion

Flexures may bend in various ways as a means of moving a linkage setthrough a range of motion. FIGS. 6A-6D illustrate various flexuremotions, including rectilinear (FIGS. 6C and 6F) and rotational (FIG.6B). In the flexure illustrations, a fixed block is shown on the top anda moving block, shown on the bottom, moves from a left-to-right orright-to-left position. In several of the illustrated movements, themoving block displaces vertically as it moves from left-to-right orright-to-left (in the figure). The linear motion illustrated in FIG. 6Cdoes not displace vertically as it moves from one position to another.

Individual beam flexures typically do not provide the potential forlinear motion unless the flexure (a) incorporates a bend or bow into thethin direction of the cross section of the flexure, (b) allows a regionof the thin direction of the cross section to buckle or “oilcan”, or (c)is combined into a set of flexures, as shown in FIG. 6F, where theflexible beams of all flexures are parallel. As shown in FIG. 6C, in anytranslation condition where a single flexure allows linear motion thereis a resulting extension or compression of the flexure normal to thedirection of motion. Causing a flexure to oilcan may significantlydeteriorate the flexure's ability to control the direction of motionbecause the flexure must form multiple inverse bends.

One way of moving a carriage in relations to a fixed base is throughrectilinear motion. Rectilinear motion is linear motion produced byforcing one rigid element to move or translate in relation to anotherrigid element by deforming or flexing the flexure opposed to justbending the flexure between the rigid elements. FIG. 6C illustrates therectilinear motion of one rigid element with respect to another rigidelement; the flexure between the two rigid elements deforms or flexes asopposed to simply bending.

FIG. 6E illustrates plan and isometric views of a fine-positioning notchflexure in a two-dimensional linkage (the linkages are 180 degreesopposed) that simply bends the flexures between a fixed base and amoving carriage to produce rectilinear motion of the moving carriage.FIG. 6F illustrates plan and isometric views of a fine-positioning bladeflexure that produces rectilinear motion in a two-dimensional linkage totranslate a moving carriage relative to a fixed base by deforming orflexing the blade flexures between the fixed base and the movingcarriage. Typically flexures are combined serially in pairs and attachedas opposing sets at the carriage corners to the base. In the illustratedarrangements, all beam flexures are parallel to each other.

The two fine-positioning blade flexures illustrated in FIGS. 6E and 6Finclude flexures that are arranged in a two-dimensional symmetricalarrangement. The arrangement is symmetrical because in one plane, oneside of the arrangement mirrors the other.

V. Design Limitations of Straight-Line Mechanisms

The inventors of embodiments of the present disclosure have identifiedthat existing linkages, when used for translating motion in a linearstage, include some design limitations. If not compensated for, thesedesign limitations can disadvantageously produce parasitic orunpredictable motion that may negatively impact the performance of alinear-motion stage. These design limitations include: parasitic effectscaused by hinges or bearings, non-linear motion caused by a flexure'schange of force as it moves through a range of motion, negativeconsequences of using an assembly of parts, and non-linear motion causedby a biased center-of-gravity.

A. Hinges and Bearings

A linkage set may include hinges or bearings. Hinges and bearings canimpose a change in force over their range motion due to changes insurface finish or friction between surfaces that move relative to eachother. As such, there can be variation in forces against a moving stageover its travel range and a build-up of forces that may cause parasiticor non-linear motion of the moving stage.

Hinges and bearings are subject to hysteresis or non-repeatable motionbecause they are made of an assembly of parts that interact at theirsliding surfaces. Those stresses may be created during assembly,alignment, or operation. Hysteresis may also be caused by plasticdeformation of materials or changes in surface properties. For example,optical systems are often used in environments that undergo largetemperature excursions. Specifically, cryogenic optics may operate attemperatures well below ambient, sometimes at only a few degrees Kelvin,from about 4 degrees Kelvin to 80 degrees Kelvin, or several hundredKelvin. Temperature excursions can cause material shrinkage orexpansion, gap or fit changes between mating components, and changes insurface friction properties. These property changes can create differenthysteresis or non-repeatable motion effects with differing operating(e.g., temperature) conditions.

Meanwhile, devices must be manufactured and set up by human beingsoperating at standard atmospheric temperatures and pressures. At everyjoint, thermal stresses and unpredictable stick, slip, or both may occurdue to residual stresses from fastening, thermal expansion andcontraction of components, or both. Moreover, the surface finish onsliding components causes stiction and friction. Stiction is the staticor threshold force that must be overcome to enable movement between twosliding surfaces.

Stiction is not predictable and may change over time. Changes intemperature during the life of an instrument often cause variations innet expansion or contraction of materials as a result of componenttemperature differences, material property differences, e.g., differentcoefficients of thermal expansion, and usually both. Accordingly, overtime, and over temperature, various additional stresses may be induced,relieved, or both. Thus, variation in temperature may cause a change instiction. That variation in stiction can disadvantageously impact theperformance of linear stage as the linear motion of the moving stage canbe unpredictable or “jerky”.

For example, in the case of an interferometer, a linear-motion stageattempts to move the carriage at constant velocity or accelerationthrough its range of motion. Stiction can create unpredictable movingmirror velocity or acceleration changes. As described above with regardsto a Michelson interferometer, a Fourier transform may be used totransform the interferogram's signal in the time domain to a frequencydomain. If a moving mirror's velocity is unpredictable or jerky, thetime domain may not translate well to the frequency domain, which maycreate noise or errors in spectrum measurements.

B. A Flexure's Change in Force Over its Range of Motion

Flexures may be used between linkages to provide the range of motion ina linkage set in a linear-motion stage. A flexure has a spring constantthat generates a force when the flexure is not in its neutral position.The spring force changes as a flexure moves through its range of motion.The spring-force change primarily applies to the moving linkage'sdirection of travel. For example, a slight bend in a flexure thatproduces only a small movement of an attached linkage (or rigid member)requires only a small force. In contrast, a large bend or movement thatproduces a large movement of an attached linkage can require a largeforce.

The spring-force change also applies to directions other than thedirection of travel. Also, the difference in force, e.g., pushing orpulling, in a direction other than the direction of travel, as a flexuremoves between a small bend and a large bend, may not be linear. Thischange in force or variation can induce non-linear motion or shear. Forexample, referring back to FIGS. 6A-6D, as the moving block in eachillustration moves from left-to-right or right-to-left, the flexureconnecting the fixed block to the moving block exerts a positive ornegative vertical (as oriented in the illustration) force on the movingblock with respect to the fixed block. This force may cause the movingblock to displace vertically, or in a non-linear or shear motion,through the flexure's range of motion. The moving block may displacevertically unless other forces are applied to the moving block to holdor constrain the moving block's vertical displacement. Within the linearstage of an interferometer, the non-linear motion can cause an angulardeviation (tilt) or lateral displacement (shear) of a reflected beamfrom a moving carriage. The angular deviation or lateral displacement ofa reflected beam can degrade an interferometer's performance.

Also in an interferometer, a drive or motor typically provides the forcethat moves the carriage in relation to the base. Ideally, in someapplications such as an interferometer, a linear-motion stage attemptsto move the carriage at a constant velocity or acceleration through itsrange of motion. Because a flexure changes in force over its range ofmotion, and that force change may be non-linear, a drive or motor maynot be able to fully compensate for the non-linear forces acting on thecarriage through its range of motion. Thus, the carriage may accelerateor decelerate unpredictably through its range of motion. In aninterferometer application, the carriage's change in velocity orunpredictable velocity or acceleration can degrade the interferometer'sperformance.

C. An Assembly of Parts

A multiple-arm linkage used in a linear-motion stage may be made up ofan assembly of parts. In an optical system, like an interferometer, eachcomponent must be positioned and aligned. Specific displacements andangles between optical elements along an optical path must typically bealigned as precisely as the requirements of the optical system. Variousalignment mechanisms are used to assure alignment of the variouscomponents. Each component must be accurately positioned with respect tothe intended propagation direction of electromagnetic radiation, e.g.,light, at whatever frequency.

The accuracy to which optical elements are initially positioned greatlyinfluences the quality or precision of the system. Potential positionerrors may be induced in an assembly of parts during assembly,alignment, adjustment, calibration, or operation of the components. Thealignment process itself is meticulous as each joint that is released ordecoupled from other components in order to move a component maymiss-align in more than one degree of freedom. Thus, the alignmentprocess is time consuming.

Additionally, individual parts are machined or manufactured with theirrespective variation and tolerances. Even the manufacturing of a singlepart requiring multiple machine set-ups or operations can createtolerance stack-up. Tolerance stack-up can induce parasitic motion orunpredictable velocity in the moving carriage of an interferometer.

D. Biased Center-of-Gravity

The moving carriage in linear-motion stage may have a center-of-gravity(CG) that is not centered on or at the carriage support points. Ineither a gravity or microgravity environment, if the CG of a movingcarriage is biased towards one side, the moving carriage may move withunpredictable shear and tilt. A non-centered CG may also causeunpredictable motion due to the variation in spring-flexure forceapplied to the carriage as the carriage travels through its range ofmotion.

VI. Possible Solutions

The inventors of embodiments of the present disclosure have identifiedthe need for a higher precision linear-motion stage. A high-precisionlinear-motion stage may be used to translate a mirror in aninterferometer with very little shear or tilt. The inventors havefurther identified several disadvantages of using the above-describedmechanisms for providing high-precision linear motion. The inventorshave identified several possible solutions, portions of which may becombined, to overcome the design limitations described above. Thesesolutions include: angular symmetry or asymmetry, radial symmetry orasymmetry, a monolithic design, or combinations thereof.

A. An Angularly Symmetric or Asymmetric Linkage

A linkage set used in a linear-motion stage may be arranged angularlysymmetric or asymmetric. FIGS. 7A, 7B, and 7C illustrate a side,isometric, and end views view of angularly asymmetric double-armlinkages, respectively. Similar to FIGS. 4B and 4C, the fixed end ofeach double-arm linkage is illustrated with a filled-in circle or dotand the moving end is illustrated as a cross. In FIGS. 7A and 7B, thedashed lines illustrate different positions of the double-arm linkageswith the moving end extended to different positions. The arrangementsillustrated in the FIGS. 7A, and 7B are angularly asymmetric because theangle formed between a first rigid element and the plane transverse tothe travel direction is not equal to the angle formed between a secondrigid element and the plane transverse to the travel direction. In otherwords, the “First Angle” is not equal to the “Second Angle” throughoutthe linkages' range of motion. This is also true for multiple-armlinkages containing more than two rigid elements if the angles betweenat least two of the rigid elements and the plane transverse to thetravel direction are not equal through the linkages' range of motion.

The double-arm linkage set in FIG. 7A and linkage sets in FIG. 7B arealso angularly asymmetric because the fixed point, illustrated as afilled-in circle or dot, of the first arm does not lie along the linearmotion path of the moving end of the second arm. This is also true forFIG. 7C but is not shown because of the end-view viewing angel. Thedouble arm-linkage set embodiment illustrated in FIG. 7B is alsoangularly asymmetric because the arms or rigid elements within eachlinkage set are a different length. A multiple-arm linkage will beangularly asymmetric if the attachment point of one arm to a base (e.g.,the “dot” in FIG. 7B) does not lie along the linear motion path of themoving end of the second arm or the arms are different lengths. Also, amultiple-arm linkage with an odd number of arms will also be angularlyasymmetric. The angularly asymmetric linkage set in FIG. 7B, withunequal arm lengths in each double-arm linkage, is different than theSarrus linkage illustrated in FIG. 4C, which has equal arm lengths.

The example doubl-arm linkages in FIG. 7B are arranged orthogonal toeach other. One double-arm linkage constrains motion of the moving crossin X-Y plane and the other double-arm linkage constrains motion of themoving cross in the Y-Z plane. The X-Y plane and the Y-Z plane intersectalong the y-axis. Combined, the two double-arm linkages constrain motionof the cross along a line illustrated as parallel to the y-axis.

A linkage assembly manufactured with flexures may have some operationaldisadvantages that, if not compensated for through other design elementsof the linkages, can disadvantageously produce parasitic orunpredictable motion that may negatively impact the performance of alinear-motion stage. For example, if a linkage assembly is manufacturedusing flexures, the flexures' arrangement can cause non-linear motiondue to lateral forces (e.g., a force component perpendicular to thetravel direction) exerted by the flexures on the moving stage throughthe flexures' range of motion.

B. A Radially Asymmetric Arrangement

A linkage set used in a linear-motion stage may be arranged radiallysymmetric or asymmetric. The linkage sets in FIG. 7B are arrangedradially asymmetric about the travel direction. The linkage set in FIG.7B includes a double-arm linkage that extends in the positive (shownextending up) Y-Z plane and another double-arm linkage that extends inthe positive (shown extending out of the page) X-Y plane. The linkageset in FIG. 7B is radially asymmetric because there are notcorresponding double-arm linkages extending in the negative Y-Z and X-Yplanes.

Radially asymmetric doubl-arm linkages like those illustrated in FIG. 7Bcan be, but need not be, arranged orthogonal relative to each other toconstrain motion of a moving carriage along a line. For example, FIG. 7Cillustrates an end view of two double-arm linkages arranged non-parallelrelative to each other. In FIG. 7C, the dashed line illustratesdifferent possible radial asymmetric positions of one double-arm linkagewith respect to the other double-arm linkage. One double-arm linkage setis illustrated as being in the X-Y plane and constrains motion of thecross to movement in the X-Y plane. The other double-arm linkage set isillustrated as being in a plane that is non-parallel to the X-Y planebut parallel to the y-axis. The other double-arm linkage set constrainsmotion of the cross to the non-parallel plane. Together, the twodouble-arm linkages constrain motion of the cross to a line, illustratedin this example as the y-axis.

In FIG. 7C, the angle between two double-arm linkages is greater thanzero and less than 180 degrees (e.g., non-parallel), and is sufficientlynon-parallel to constrain motion of the cross to a line. The anglebetween two double-arm linkages need only be sufficiently non-parallelto constrain motion of a moving carriage to a line. For example, theangle between the two double-arm linkages can be any angle that is notzero and not 180 degrees to constrain motion of a moving carriage to aline, depending on other design elements of the double-arm linkages.

As described above, a flexure's force, acting both along the directionof travel and in other directions, e.g., lateral directions, changesthrough the double-arm linkage's or moving carriage's range of motion.These changes in lateral force can create non-linear motion or shear andtilt in a radially asymmetric configuration because symmetricallyopposing linkages are not available to counteract the changes in forcethrough the flexures' range of motion.

However, the inventors of the present disclosure have discovered thatfor a radially asymmetric arrangement, lateral forces acting on thecarriage can be compensated for by providing: (a) linkage arms ofdifferent lengths, e.g., angular asymmetry, (b) a fixed end that doesnot lie along the linear motion path (or line) of the moving end (alsoangular asymmetry), (c) different angles between the arms of a linkage(also angular asymmetry), (d) varying the spring constants or springrates of the flexures themselves, or (e) varying the initial anglesbetween the linkage arms at the neutral position (also angularasymmetry). Any of these arrangements or design options may be used,alone or in combination, to compensate for changes in lateral (e.g.,perpendicular) forces over the travel range such that the resultingmotion of a moving stage relative to the base can be linear andpredictable. When using flexures, lateral-force compensation ensures,and is usually necessary, for a linear-stage design to move in a linearmotion. The changes in lateral forces are likely the reason why aradially asymmetric Sarrus linkage, used as a linear motion stage orprecision linear actuation, has not previously incorporated flexures inits design.

C. A Radially Symmetric Arrangement

A radially symmetric design can have several advantages. First, becausethe arrangement is symmetrical, the rigid segment and flexure linkagesets cancel forces that lead to parasitic motion. FIGS. 8A, 8B, and 8Cillustrate end, side, and isometric view, respectively, of a three-armradially symmetric linear-motion stage 300. FIGS. 9A, 9B, and 9Cillustrate an end, side, and isometric view, respectively, of a four-armradially symmetric monolithic linear-motion stage 400.

Radially symmetric configurations with opposing linkage sets or opposingflexure arrangements like those illustrated in FIGS. 8A-9C may includeflexures that change in force through their range of motion. Eachflexure in the fine-positioning linear stages induces a change in forcethat is applied to the moving carriage over its range of motion. Thatforce is directed along the line of motion and in other directions notalong the line of motion, e.g., perpendicular to the line of motion.Those forces can cause non-linear motion or shear of the movingcarriage. The radially symmetric arrangement works well because thechange in force from one flexure cancels the change in force of itsopposing flexure or flexures. The resulting motion of the stage relativeto the base can therefore be linear and predictable.

However, a radially symmetrical arrangement also has some disadvantages.First, it may be difficult to manufacture a three-dimensional, radiallysymmetric linkage that is monolithically and homogenously formed from asingle material. Additionally, the radially symmetric arrangement mayoccupy a larger volume and have a greater weight as compared to aradially asymmetric arrangement. Several of these disadvantages may beovercome by using angular asymmetric linkage sets as described above.

D. An Assembly of Parts or a Monolithic Arrangement

A linkage assembly of parts has some assembly and operationaldisadvantages. An assembly of parts includes multiple parts, i.e., moreparts to manufacture and more tolerance stacking. An assembly of partscan also be difficult to assemble and mechanically or optically align. Alinkage assembly made of hinges or bearings also comes with itsassociated problems of hysteresis, friction, or stiction, each of whichproduces non-repeatable motion.

A linkage set used in an interferometer may be monolithically andhomogeneously formed of a single material. The linkage set may includerigid segments that are effectively blocks connected in series byflexures, the flexures and the rigid segments being formed from a singlematerial. In this configuration, no joints are used between the rigidelements and the flexures. An advantage of monolithic manufacturing isthat flexures, a linkage set, or multiple linkages can be manufacturedin a single operation to significantly reduce or eliminate tolerancestack-up, alignment error, and assembly and alignment steps and time.

VII. Examples

The following examples are illustrative only and are not intended tolimit the disclosure in any way.

A. A Linear-Motion Stage with Four Multiple-Arm Linkages

1. Application and General Description

FIG. 10A illustrates in an isometric view an embodiment of a radiallyand angularly non-symmetric, multiple-arm linear-motion stage 500 withfour multiple-arm linkages, labeled 101-104, which are circled. Inembodiments, a linear-motion stage 500 may include a base 31, a carriage41, a first carriage end 41A, a second carriage end 41B, and two or moremultiple-arm linkages.

The linear-motion stage 500 may be used in various linear-motion stageapplications. Any device may be attached to the carriage of alinear-motion stage. For example, linear-motion stage 500 may be used inmanufacturing equipment or machines including robots, machine tools,assembly, semiconductor equipment, laser equipment, electronicmanufacturing equipment, or other industrial automation applications.Linear-motion stage 500 may also be used in a variety of opticalapplications, including a microscopic stage, an optic lab stage, anoptical fiber alignment system, or as an optical stage or as aninterferometer mirror translation stage in a Fourier transformspectrometer.

Referring back to FIGS. 1A and 2A, the linear-motion stage 500 may beused to provide the mirror displacement of a corner-cube reflector 60 ora planar mirror in a Fourier transform interferometer 50. A corner-cubereflector or planar mirror may be attached to the carriage 41 or thefirst or second carriage ends 41A or 41B. Alternatively, any opticaldevice may be attached to the carriage 41 or the first or secondcarriage ends 41A or 41B to provide linear motion to the optical device.For example, an optical device may be a lens, filter, diffuser,beamsplitter, focal plane array, prism, polarizer, grating, lightsource, collimator, or other optical device.

In embodiments, the linear-motion stage 500 may provide a true linearmirror displacement (low shear and low tilt) for the corner cubereflector 60 or planar mirror in a Fourier transform interferometer 50.The base 31 may be fixed relative to other components of theinterferometer 50. The carriage 41, or carriage ends 41A or 41B, mayoscillate in a back and forth motion, as illustrated by the CarriageMotion line, relative to the base 31 and other components of theinterferometer 50. The carriage 41, or carriage ends 41A or 41B, maymove back and forth, like an oscillating spring, in a fluid, predictablemotion with little to no friction.

The linear-motion stage 500 is arranged radially asymmetric andtherefore is less voluminous and weighs less than a radially symmetriclinear-motion stage. In the illustrated embodiment, the carriage motionline 42 may be considered to run along the y-axis. In this arrangement,multiple-arm linkages 102 and 103 extend in the positive X-Y plane (intothe page) and multiple-arm linkages 101 and 104 extend towards thenegative Y-Z plane (downward). In this embodiment, the radiallyasymmetric, linear-motion stage 500 does not include four additionalmultiple-arm linkages that extend in the negative X-Y plane (out of thepage) or in the positive Y-Z plane (upward).

In multiple-arm linkage 101, the first rigid element 32 originates atthe base 31 via flexural joint 11. Rigid element 32 does not originateat a point along the carriage motion line 42. This is similar to thearrangement illustrated in FIGS. 7A and 7B. As a result, an angle formedbetween a first rigid element 32 of multiple-arm linkage 101 and a planetransverse to the carriage motion line 42, e.g., the X-Z plane, is notequal, throughout the range of motion of multiple-arm linkage 101, to anangle formed between a second rigid element 33 of multiple-arm linkage101 and the plane transverse to the carriage motion line 42. Thediffering angles may be used to compensate for changes in force over therange of motion resulting in motion that is linear.

2. Multiple-Arm Linkages

FIG. 10B illustrates an elevation view of one embodiment of amultiple-arm linkage 101, also circled in the lower-right corner of thelinear-motion stage 500 in FIG. 10A. In embodiments, a multiple-armlinkage includes three flexures or flexural joints, labeled 11, 12, and13, and two rigid members, labeled 32 and 33. The flexures and the rigidelements may be attached in series. For example, a first flexure 11 mayconnect the base 31 to the rigid element 32; a second flexure 12 mayconnect rigid element 32 to rigid element 33; and a third flexure 13 mayconnect rigid element 33 to carriage 41 or carriage end 41A. Componentsof the multiple-arm linkage 101, including the base 31 or the carriageend 41A, may be homogeneously formed of a single material, having ajoint-free continuity of the single material from the base 31, throughthe first flexure 11, rigid element 32, second flexure 12, rigid element33, and third flexure 13, to carriage attachment piece 41A.

3. Flexures and Degrees of Freedom

Flexures or flexural joints like 11, 12, or 13 allow their attachedrigid members to move, rotate, or pivot relative to each other about theflexural joint, or about a flexural axis formed by and running thelength of the flexural joint, with little to no friction. The flexuresmay be sufficiently long to constrain the motion of their attached rigidmembers to a rotating or pivoting motion, or one degree-of-freedom(DOF), about the flexural axis and constrain or prevent rotation ormovement in other degrees-of-freedom. For example, referring again toFIG. 10B, flexural joint 11 forms a flexural axis, illustrated as beingparallel to the x-axis, which is along the length of the flexural joint11, that permits rigid element 32 to rotate or pivot about flexuraljoint 11 relative to base 32 in the Y-Z plane in a one-DOF motion.Additionally, flexural joint 11 restrains or prevents the motion ofrigid element 32 in other degrees-of-freedom. Similar to flexural joint11, flexural joints 12 and 13 allow rigid element 33 and carriage end41A to pivot about rigid elements 32 and 33, respectively, in the Y-Zplane. For multiple-arm linkage 101, the Y-Z plane is the movement planeand all other planes are motion-constrained planes.

FIG. 10B illustrates multiple-arm linkage 101 in an unconstrainedposition. Flexures 11, 12 and 13, like unloaded springs, tend to holdrigid elements 32 and 33, or the multiple-arm linkage 101 in theillustrated position. To illustrate how a single flexure operates, forexample, if a one-time or repetitive force is applied to carriage end oroptics mounting plane 41A, and rigid element 33 is held in a fixedposition, carriage end 41A will oscillate with fluidic motion, like aninverted pendulum, with little to no friction, about the axis formed byflexural joint 13.

Various flexure types are available for use. For example, cross flexuressuch as cantilevered (single-ended) pivot bearings and double-endedpivot bearings, or non-cross flexures such as linear flexure bearings,all sold by Riverhawk Company of New York, may be used as flexureswithin linear-motion stage 500. Similarly, single-end or double-endbearing flexures sold from C-Flex Bearings Company of New York may alsobe used as flexures. In some instances, cross flexures, which have atleast two thin pieces of metal extending along some length of theflexural axis and arranged in the form of a cross, provide substantialrigidity in motion-constrained planes and adequate movement in themovement axis. There are other flexure designs that may also be used.

4. Multiple-Arm Linkages and Degrees of Freedom

Referring again to FIG. 10A, the multiple-arm linkages 101-104 constrainmotion of the carriage assembly (carriage 41 and carriage ends 41A and41B), with respect to base 31, along carriage motion line 42. If aone-time or repetitive force, with a component vector parallel tocarriage motion line 42, is applied to any component of the carriageassembly (carriage 41 and carriage ends 41A and 41B), the carriageassembly will oscillate left and right with respect to base 31, alongthe carriage motion line 42.

For example, in the illustrated embodiment, multiple-arm linkages 101and 104 constrain the movement of carriage 41 to movement in the Y-Zplane, or three degrees of freedom: in the y or z translationaldirections, and rotational about the x-axis. For multiple-arm linkages101 and 104, the Y-Z plane is the movement plane and all other planesare motion-constrained planes. Additionally, in the illustratedembodiment, multiple-arm linkages 102 and 103 constrain motion ofcarriage 41 to movement in the X-Y plane, or three degrees of freedom:in the x or y translational directions, and rotational about the z-axis.For multiple-arm linkages 102 and 103, the X-Y plane is the movementplane and all other planes are motion-constrained planes.

In the illustrated embodiment, the Y-Z and X-Y planes intersect at aline. That intersection line is the carriage motion line 42 or a lineparallel to the carriage motion line 42. In other words, the carriagemotion line 42 is parallel to an intersection line formed by theintersection of the Y-Z and X-Y plane. In the illustrated embodiment ofFIG. 10A, the intersection line of the Y-Z plane and the X-Y plane isthe carriage motion line 42.

When multiple-arm linkages 101-104 are combined, as in the illustratedembodiment, the linkage sets 101-104 constrain motion of the carriage 41to movement along the carriage motion line 42, or a line parallel to thecarriage motion line 42. All other lines, or lines in other directions,are motion-constrained lines. In embodiments, the carriage motion line42 is a true linear travel path or a straight line. In this embodiment,the motion of carriage end 41A (or 41B), where a mirror may be attached,is constrained in five degrees (three rotational, and two translational)of motion, and only free to move in one translational direction,illustrated as the y-axis direction. In embodiments, the inventors ofthe present disclosure have modeled a prototype carriage assembly thatis able to travel along a linear path of approximate two centimeterswith a tilt of less than one arc second and a shear less than onemicron.

5. Over-Constrained Motion

Each double-arm linkage set provides its own movement plane. Forexample, double-arm linkage set 101 provides a first movement plane,double-arm linkage set 102 provides a second movement plane, double-armlinkage set 103 provides a third movement plane, and double-arm linkageset 104 provides a fourth movement plane. In this arrangement, the firstand second movement planes are perpendicular and intersect at a line.Also, the third movement plane is perpendicular to the first movementplane and parallel to, or in the same plane as, the second movementplane. If the third movement plane does not intersect the first movementplane along a line that is parallel to the intersection of the first andsecond movement planes, the entire mechanism may be over-constrained.FIG. 2C illustrates one possible example of the plane intersections ofan over-constrained mechanism.

Described in another way, the linear-motion stage 500 may beover-constrained if the movement planes created by the linkage sets101-104 are not parallel to a common line. If over-constrained, themotion of the carriage 41, or carriage ends 41A or 41B, may benon-linear or the carriage may move in an undefined manner or along anundetermined path. This condition may cause flexure buckling, stress andstrain in the flexures, reduced life cycle, fatigue, yield, or anincrease of the energy required to move the carriage 41.

The movement plane of double-arm linkage set 103 should be parallel tothe movement plane of double-arm linkage set 102 and non-parallel, orpreferentially perpendicular, to the movement plane of double-armlinkage set 101. If that is true, the movement plane of double-armlinkage set 103 will intersect the movement plane of double-arm linkageset 101 along a line parallel to the carriage motion line 42.

6. Avoiding Over-Constrained Motion in a Linear-Motion Stage

A linear-motion stage may be manufactured in such a way as to avoidover-constrained motion. Referring again to FIGS. 10A and 10B, inembodiments, the flexural axes or the bending axes formed by flexuralelements 11, 12, and 13 within multiple-arm linkage 101 run in aparallel direction or are co-aligned to be parallel. In this sense, theflexural axes are parallel, or substantially parallel, according toachievable manufacturing tolerances associated with the machining orcutting of a multiple-arm linkage. The flexural axes formed by flexuralelements within multiple-arm linkage 101 may be similarly substantiallyparallel to the flexural axes formed by flexural elements withinmultiple-arm linkage 104.

Likewise, the flexural axes within multiple-arm linkages 102 and 103 maybe substantially orthogonal to the multiple-arm linkages 101 and 104.The flexural axes contained in one multiple-arm linkage may runparallel, orthogonal, or in other directions as compared to the flexuralaxes in other multiple-arm linkages. Typically, however, the flexuralaxes within a single multiple-arm linkage run substantially parallel toeach other in order to constrain motion to a plane.

Single or multiple multiple-arm linkages with their respective flexuresand rigid members may be manufactured through EDM (electrical dischargemachining) EDM machining involves a probe electrically charged to have apotential between the mount in which a workpiece is held, and the EDMwire (or probe) that machines the work piece. By putting sufficientelectrical potential between the mount (therefore the workpiece), andthe probe, atoms of metal may be precisely removed from a workpiece inorder to cut particular shapes.

Manufacturing the flexural axes such that they are parallel may be donein a single manufacturing operation, i.e., the workpiece is not removedfrom the mount throughout the entire manufacturing operation. Often,such machining is done in a submerged dielectric oil or water bath inorder to provide cooling, transport of the machined material, and soforth.

B. Various Multiple-Arm Linkage Arrangements

The arrangement illustrated in FIG. 10B of flexures and rigid elementswithin a linkage set, including the attachment locations of flexurallocations to rigid elements, is one embodiment of several possiblearrangements. FIGS. 11A-11E illustrate other possible multiple-armlinkage arrangements. Other arrangements based on combinations orsubsets of the arrangements illustrated in FIGS. 11A-11E are alsopossible. For example, in FIGS. 11A and 11B, the arrangement of rigidelements 32 and 33 in multiple arm linkage sets 201A and 201B, as wellas the attachment locations of flexures 11, 12, and 13 to theirrespective rigid elements, have been rearranged into a “W” shape insteadof a simple right-angle arrangement, as shown in FIG. 10B.

Also, for multiple-arm linkage 201C, illustrated in FIG. 11C, rigidelements 32 and 33 from FIG. 10B, have been divided into rigid elements32A-C and 33A-B, respectively. The additional rigid elements necessitatethree additional flexures such that multiple-arm linkage 201C includessix flexures: 11A, 11B, 12, 13A, 13B, and 13C. The increased number ofrigid elements and flexures allows for greater travel distance ofcarriage attachment piece 41A in the Y-Z plane and thus a greater traveldistance for an optical component attached to carriage attachment piece41A along a line parallel to the y-axis. However, the increased numberof rigid elements and flexures may decrease the rigidity of themultiple-arm linkage 201C. For a multiple-arm linkage, by rigid is meantthat the linkage set's section moduli in the non-motion ormotion-constrained planes is substantially greater than the linkageset's section modulus in the movement plane. In other words, by rigidityis meant the ability of the multiple-arm linkage to allow motion in themovement plane and constrain motion in other planes.

FIG. 11D illustrates multiple-arm linkage 201D, which arranges rigidelements 32D and 33C away from base 31 and then back towards carriageattachment piece 41A. In FIG. 11E, multiple-arm linkage 201E includesadditional rigid elements 32E-G and flexures 12A-12C, arranged in anaccordion-like shape. Like the other multiple-arm linkages withadditional rigid members and flexures, multiple-arm linkage 201Eprovides greater mobility in the Y-Z plane and thus greater traveldistance for an optical component attached to carriage attachment piece41A along a line parallel to the y-axis. However, multiple-arm linkage201E may also have decreased rigidity if greater optical travel distanceis required.

The section modulus of any flexure within a multiple-arm linkageillustrated in FIG. 10B or 11A-11E need not be the same as the sectionmoduli of any other flexures in the same multiple-arm linkage. If thesection modulus of the first flexure is greater than the section modulusof other flexures, the entire multiple-arm linkage will be more rigid.For example, having a first flexure with an increased section modulusand having other flexures in the same multiple-arm linkage withdecreased section moduli in their bending directions may provide amultiple-arm linkage that is rigid but is also capable of greater travelin the multiple-arm linkage's movement plane.

The rigid elements 32 and 33 of multiple-arm linkage 201A and rigidelements 32′ and 33′ of multiple-arm linkage 201B are arrangedorthogonally relative to each other. Rigid elements 32 and 33 aresomewhat similar in length to each other, however rigid elements 32′ and33′ are not similar in length to each other. The more orthogonal a first(32 or 32′) and second (33 or 33′) arm of a linkage, the less similar inlength they need to be. Rigid element 33′ may be greater than 25% longerthan rigid element 32′. In contrast, rigid elements 32D and 33C ofmultiple-arm linkage 201D and rigid elements 32F and 33G of multiple-armlinkage 201E are arranged nearly parallel to each other. Assuming thespacing along the Z-axis between the base 31 and the carriage 41A doesnot change, the more parallel the first (32D or 32F) and second (33C or33G) arm of multiple-arm linkage, the more similar in length the armsneed to be.

C. A Linear-Motion Stage with Fewer Multiple-Arm Linkages

A linear-motion stage may have fewer multiple-arm linkages than thoseillustrated in FIG. 10A. A linear-motion stage with two multiple-armlinkages may still constrain motion of a carriage along a true lineartravel path so long as the flexures are sufficiently rigid or themultiple-arm linkage linear carriage is sufficiently balanced, e.g.,there is not a biased center-of-gravity.

For example, FIG. 12A illustrates a linear-motion stage 600 with a base31, two multiple-arm linkages 101 and 102, and carriage attachment piece41A. Base 31, multiple-arm linkages 101 and 102, and carriage attachmentpiece 41A are the same as those illustrated in FIG. 10A. Multiple-armlinkage 101 includes rigid elements 32 and 33 and flexures 11, 12, and13. Multiple-arm linkage 101 constrains the motion of carriage end 41Ato motion in the Y-Z plane, or a plane parallel to the Y-Z plane,because the flexural axes formed by flexures 11, 12, and 13 run parallelto each other and the x-axis (or a line parallel to the x-axis). Formultiple-arm linkage 101, the Y-Z plane is the movement plane and allother planes are motion-constrained planes. Multiple-arm linkage 102includes rigid elements 34 and 35 and flexures 14, 15, and 16.Multiple-arm linkage 102 constrains motion of carriage end or opticsmounting piece 41A in the X-Y plane, or a plane parallel to the X-Yplane, because the flexural axes formed by flexures 14, 15, and 16 runparallel to each other and the z-axis (or a line parallel to thez-axis). For multiple-arm linkage 102, the X-Y plane is the movementplane and all other planes are motion-constrained planes.

In the illustrated embodiment, flexures 13 and 14, or the flexural axes(e.g., rotation axes or lines) of flexures 13 and 14, form a connectionor balancing plane in the X-Z plane, labeled 41A_(P1). In this case,Plane 41A_(P1) and the surface of carriage end 41A are parallel to theX-Z plane. The center of gravity of optics mounting piece 41A is locatedat the center of balancing plane 41A_(P1). In this sense, carriagemounting piece 41A is balanced at the center of its attached flexures 13and 14. Because the center of gravity of carriage mounting piece 41A isbalanced, the flexures within multiple-arm linkages 101 and 102 are verylikely to be sufficiently rigid to constrain motion of carriage mountingpiece 41A along a line parallel to the intersection of the Y-Z and X-Yplane, illustrated as the carriage motion line 42. As the carriagemotion line 42 is a straight line, there is no lateral displacement,shear, or tilt of the carriage attachment piece 41A as it travels alongthe carriage motion line 42. Therefore a mirror attached to carriagemounting piece 41A will be configured to reflect a beam with very littleto no shear or tilt.

Carriage attachment piece 41A may be configured to be balanced, evenwith the addition of a mirror or mirrors, e.g., planar mirror 55 orcorner-cube reflector 60 illustrated in FIG. 1A or 1B, attached tocarriage mounting piece 41A. If balanced, plane 41A_(P1) and the surfaceof carriage mounting piece 41A will remain parallel to the X-Z plane ascarriage mounting piece 41A moves along the carriage motion line 42. Ifcarriage attachment piece 41A is not balanced, plane 41A_(P1) and thesurface of carriage mounting piece 41A may tilt relative to the X-Zplane as carriage mounting piece 41A moves along the carriage motionline 42.

Multiple-arm linkages need not attach to a carriage mounting piece inthe same plane as illustrated in FIG. 12 A. For example, FIG. 12Billustrates linear motion stage 600 a with multiple-arm linkages 101 and102 a. Multiple-arm linkage 101 attaches to carriage mounting piece 41A′through flexure 13 along a line parallel to plane 41A_(P1), similar tolinear motion stage 600 illustrated in FIG. 12A. However, multiple-armlinkage 102 a attaches to carriage mounting piece 41A′ through flexure14 along a line parallel to plane 41A_(P2). Planes 41A_(P1) and 41A_(P2)are offset some distance from each other along carriage motion line 42.

FIG. 13 illustrates a linear-motion stage 700 that includes the samecomponents as linear-motion stage 600 in FIG. 12. Linear-motion stage700 additionally includes a carriage 41 and carriage attachment piece41B. Multiple-arm linkage 101 extends from the base 31 to first carriageattachment piece 41A; multiple-arm linkage 102 extends from firstcarriage attachment piece 41A to the base 31. Second carriage attachmentpiece 41B is offset some distance along the carriage motion line 42 fromfirst carriage attachment piece 41A but there is no multiple-arm linkageconnecting the second carriage attachment piece 41B to the base 31. Incontrast to linear-motion stage 600 in FIG. 12, the center of gravity ofthe combined carriage 41 and carriage attachment pieces 41A and 41B inlinear-motion stage 700 is displaced a distance from the carriageattachment piece or end 41A.

In a gravity or microgravity environment, the weight or gravity force ofthe carriage 41 and carriage end 41B (illustrated as F_(G)), or any massnot centered on balancing plane 41A_(P1), tends to pull the carriage 41away from the carriage motion line 42 such that carriage 41 pivots aboutcarriage attachment piece 41A. Under these conditions, if the flexuresare not sufficiently rigid to maintain the position of the carriage 41along a line parallel to an intersection line of the Y-Z and X-Y planes,plane 41A_(P1) and the surface of carriage mounting piece 41A will tiltrelative to the X-Z plane as carriage mounting piece 41A moves along thecarriage motion line 42. Also, the oscillating motion of the carriageattachment piece 41A may not be in a true linear path or along theillustrated carriage motion line 42.

If, however, the flexures are sufficiently rigid to maintain theposition of the carriage 41 along a line parallel to an intersectionline of the Y-Z and X-Y planes (e.g., the carriage motion line 42), orif a counter-balance weight is applied such that the center of gravityof the carriage assembly is balanced at balancing plane 41A_(P1), thenthe surface of carriage mounting piece 41A will remain parallel to theX-Z plane as carriage mounting piece 41A moves along the carriage motionline 42. In addition, carriage attachment piece 41A will be able tooscillate or travel along a true linear path that is parallel to a lineformed by the intersection of the Y-Z and X-Y planes, or along thecarriage motion line 42. Whether linear-motion stage 700 is configuredto maintain little to no shear and restrict motion of its carriage 41,or first carriage end 41A, along a true linear path is a function of therigidity of the flexures and the amount of moment-arm created by a forcepositioned some distance from balancing plane 41A_(P1). An unbalancedcarriage tends to be more susceptible to vibration-induced parasitic ornon-linear motion than a balanced carriage. When vibrating, the centerof mass of the carriage will tend to rotate out of the constrained planeabout the attachment point, or about the centroid location of multipleattachment points constraining motion to a given constraint plane.

In some embodiments, three multiple-arm linkages may be desirable toconstrain motion of a carriage along a true linear travel path. FIG. 14illustrates an alternative arrangement of a linear-motion stage 800 thatincludes three multiple-arm linkages 101-103. Multiple-arm linkage 101extends from the base 31 to first carriage end 41A; multiple-arm linkage102 extends from first carriage end 41A to the base 31; and multiple-armlinkage 103 extends from the base 31 to second carriage end 41B. Secondcarriage end 41B is offset some distance along the carriage motion line42 from first carriage end 41A.

Multiple-arm linkage 101 constrains the movement of carriage 41 andcarriage ends 41A to movement in the Y-Z plane. Multiple-arm linkage 101additionally constrains the movement of second carriage end 41B ifflexural joint 13 is long. In this arrangement, the Y-Z plane is themovement plane and all other planes are motion-constrained planes.Additionally, multiple-arm linkages 102 and 103 support the mass andconstrain the motion of carriage 41 to movement in the X-Y plane, i.e.,the X-Y plane is the movement plane and all other planes aremotion-constrained planes. Multiple-arm linkages 101-103 are sufficientto constrain motion of carriage 41 along a true linear travel path. Inthis embodiment, the third multiple-arm linkage, multiple-arm linkage103, makes up for flexures that may not be sufficiently rigid so as toprevent twisting motion of carriage 41 due to the moment-arm created bythe weight of carriage 41 offset some distance from balancing plane41A_(P1).

FIG. 15A illustrates the linear-motion stage 500 with four multiple-armlinkages 101-104, labeled with their respective rigid members andflexures. In this embodiment, multiple-arm linkage 101 connects the base31 to first carriage end 41A and includes first flexure 11, rigid member32, second flexure 12, rigid member 33, and third flexure 13, allconnected in series. Multiple-arm linkage 102 connects first carriageend 41A to the base 31 and includes fourth flexure 14, rigid member 34,fifth flexure 15, rigid member 35, and sixth flexure 16, all connectedin series. Multiple-arm linkage 103 connects the base 31 to secondcarriage end 41B and includes seventh flexure 17, rigid member 36,eighth flexure 18, rigid member 37, and ninth flexure 19, all connectedin series. Finally, multiple-arm linkage 104 connects second carriageend 41B to the base 31 and includes tenth flexure 20, rigid member 38,eleventh flexure 21, rigid member 39, and twelfth flexure 22, allconnected in series. All the components in linear-motion stage 500 maybe manufactured from a single, monolithic, integral, or homogeneouspiece of material.

In the illustrated embodiment of linear-motion stage 500, flexures 11-13and 20-22 have flexural axes or the bending axes that run parallel, orsubstantially parallel to each other, or the x-axis. Similarly, flexures14-19 have flexural axes that run parallel, or substantially parallel toeach other or the z-axis. In FIG. 15A, the x-axis and the z-axis areorthogonal, or substantially orthogonal, so the flexural axes offlexures 11-13 and 20-22 run orthogonal to the flexural axes of flexures14-19. In this description, “parallel” or “substantially parallel,” and“orthogonal” or “substantially orthogonal” is meant that the flexuralaxes are manufactured parallel or orthogonal according to achievable orreasonable manufacturing tolerances.

Multiple-arm linkages may attach to a carriage or carriage end anywherealong a line parallel to the carriage motion line. For example, FIG. 15Billustrates linear motion stage 500 a with multiple-arm linkages 101,102 a, 103, and 104 a. Multiple-arm linkage 101 attaches to carriagemounting piece 41A′ through flexure 13 along a line parallel to plane41A_(P1), similar to linear motion stage 500 illustrated in FIG. 15A.Similarly, multiple-arm linkage 103 attaches to carriage mounting piece41B′ through flexure 19 along a line parallel to plane 41B_(P2), similarto linear motion stage 500 illustrated in FIG. 15A. In contrast tolinear motion stage 500, multiple-arm linkages 102 a and 104 a in linearmotion stage 500 a attach to carriage mounting pieces 41A′ and 41B′ atdifferent locations. For example, multiple-arm linkage 102 a attaches tocarriage mounting piece 41A′ through flexure 14 along a line parallel to41A_(P2) and multiple-arm linkage 104 a attaches to carriage mountingpiece 41B′ through flexure 20 along a line parallel to 41B_(P1). Planes41A_(P1), 41A_(P2), 41B_(P1), and 41B_(P2) are parallel to each otherand offset some distance from each other along carriage motion line 42.

FIGS. 16A-16C illustrate a top, elevation, and side view oflinear-motion stage 500. The multiple-arm linkages 101-104 are notlabeled but their respective rigid members and flexures are. FIGS.16A-16C provide additional perspective views to the other isometricviews of linear-motion stage 500.

FIGS. 17A and 17B illustrate top and elevation views, respectively, ofportions of linear-motion stage 500. For clarity, in FIG. 17A, onlymultiple-arm linkages 102 and 103, together with carriage 41, carriageends 41A and 41B, and base 31, are illustrated. Likewise in FIG. 17B,only multiple-arm linkages 101 and 104, together with carriage 41,carriage ends 41A and 41B, and base 31, are illustrated. FIGS. 17A and17B illustrate the carriage 41 shifted right along the carriage motionline 42. The dashed outlines of rigid elements 32-35 and 38-39 andcarriage attachment pieces 41A and 41B are the original positions of therespective members with the carriage 41 at its center position. FIGS.17A and 17B illustrate how the rigid elements pivot around flexural axesas the carriage 41 moves from a center position to a right position.FIGS. 17A and 17B also illustrate how a corner cube reflector 60,another optics device, or any device may be attached to a carriageattachment piece 41A.

D. A Radially Symmetric Monolithic Linear-Motion Stage

FIG. 18A illustrates an isometric view of a three-arm, radiallysymmetric, monolithic, linear-motion stage 300, also shown in differentviews in FIGS. 8A-8C. FIG. 18B illustrates an elevation view oflinear-motion stage 300. In the elevation view of FIG. 18B, someelements obscure the view of other elements of linear-motion stage 300.

While all elements of multiple-arm linkage 301 are shown, only someelements are numbered in FIGS. 18A and 18B. In this embodiment,linear-motion stage 300 includes a base 331 having a proximal base end331 a and a distal base end 331 b. Linear motion stage 300 furthercomprises a carriage 341 having a proximal carriage end 341 a and adistal carriage end 341 b. Linear motion stage 300 further includesthree multiple-arm linkages 301, 302, and 303. In this embodiment,multiple-arm linkages 301, 302, and 303 each have the same componentsand configuration. Each multiple-arm linkage 301, 302, and 303 includesa linking rigid element 334 that has a proximal attachment end 334 a anda distal attachment end 334 b (both circled with a dashed line). Forclarity, only the proximal attachment end 334 a and the distalattachment end 334 b of linking rigid element 334 in multiple armlinkage 301 are labeled in FIG. 18A.

The proximal attachment end 334 a connects the proximal base end 331 ato the proximal carriage end 341 a through the linking rigid element334. Similarly, the distal attachment end 334 b connects the distal baseend 331 b to the distal carriage end 341 b through the linking rigidelement 334.

In the illustrated embodiment of linear-motion stage 300, multiple-armlinkages 301, 302, and 303 are homogeneously formed of a singlematerial, having a joint-free continuity of the single material throughflexures and rigid elements.

Referring to distal attachment end 334 b of multiple-arm linkage 301 inFIGS. 18A and 18B, multiple-arm linkage 301 includes a first flexure 311extending from the distal base end 331 b to a first rigid element 332, asecond flexure 312 extending from the first rigid element 332 to thelinking rigid element 334, a third flexure 313 extending from thelinking rigid element 334 to a second rigid element 333, and a fourthflexure 314 extending from the second rigid element 333 to the distalcarriage end 341 b. The proximate end 334 a of multiple-arm linkage 301also includes corresponding flexures, the proximal attachment end 334 aof linking rigid element 334, and rigid elements that connect theproximal base end 331 through the linking rigid element 334 to theproximal carriage end 341 a.

In linear-motion stage 300, multiple-arm linkages 301, 302, and 303 areradially symmetric about the carriage motion line 42, 120 degrees apartfrom each other. The three multiple-arm linkages 301, 302, and 303 eachconstrain motion of the carriage 341 to first, second, and thirdmotion-constrained planes, illustrated and labeled as 301 p, 302 p, and303 p.

The three motion-constrained planes 301 p, 302 p, and 303 p, areillustrated as extending beyond linear motion stage 300 and are furtherillustrated as being parallel to the carriage-motion line 42. Forillustration purposes only, FIG. 18A shows the carriage motion line 42as extending beyond the base 331, however, the carriage motion, in thisillustrated embodiment, does not extend beyond the base 331. In thisspecific embodiment, motion-constrained planes 301 p, 302 p, and 303 pintersect at carriage-motion line 42. In this illustration, the carriagemotion line 42 is parallel to the x-axis. Multiple-arm linkages 301,302, and 303, combined, constrain motion of the carriage 341 along thecarriage motion line 42, or a line parallel to the carriage motion line42. To properly constrain motion to a line, motion-constrained planesshould be parallel to the line; the motion-constrained planes need notintersect at the line.

FIGS. 19A and 19C illustrate isometric and side views, respectively, ofanother three-arm radially symmetric monolithic linear-motion stage 310.Like linear-motion stage 300, linear-motion stage 310 includes a base331 (with proximal and distal base ends not labeled) and threemultiple-arm linkages 301 a, 302 a, and 303 a, radially spaced 120degrees apart from each other around a carriage 341. Each multiple-armlinkage 301 a, 302 a, and 303 a constrains motion of the carriage 341along a plane parallel to the orientation of the respective multiple armlinkage set. The motion-constrained planes of multiple-arm linkages 301,302, and 303 are parallel to a carriage-motion line 42, or a lineparallel to the carriage motion line 42.

Linear-motion stage 310 differs from linear-motion stage 300 byreplacing rigid elements and flexures extending between the base 331 andthe linking rigid element 334 of each multiple-arm linkage 301 a, 302 a,and 303 a, with single blade flexures. For example, one end ofmultiple-arm linkage 301 a includes a blade flexure 311 a that extendsfrom the base 331 to the linking rigid element 334 and another bladeflexure 312 a that extends from the linking rigid element 334 to thecarriage 341.

FIG. 19B illustrates an isometric view of another three-arm radiallysymmetric monolithic linear-motion stage 310 a. Linear-motion stage 310a includes a shaft 361 that extends from the carriage 341 a, through ahole in the base 331 a, beyond the base 331 a. The shaft 361 may be usedto attach any device intended to travel along the carriage motion line42 with very low tilt or shear. A shaft similar to shaft 361 and acorresponding hole in a base may be added to any linear-motion stagedescribed in this disclosure to enable linear motion travel beyond anybase of any linear-motion stage.

FIGS. 20A and 20B illustrate an isometric and side view, respectively,of a four-arm, radially symmetric, monolithic, linear-motion stage 400,also shown in various views in FIGS. 9A-9C. In this embodiment,linear-motion stage 400 includes a base 431, four multiple-arm linkages401, 402, 403, and 404, and a carriage 441. In the side-elevation viewof FIG. 20B, multiple-arm linkage 402 obscures the view of multiple-armlinkage 404.

While all elements of multiple-arm linkage 401 are shown, only someelements are numbered in FIG. 20B. Multiple-arm linkages 401-404 eachhave the same components and configuration. Referring to the distal end(not circled) of multiple-arm linkage 401 in FIG. 20B, multiple-armlinkage 401 includes a first flexure 411 extending from the base 431 toa first rigid element 432, a second flexure 412 extending from the firstrigid element 432 to linking rigid element 434, a third flexure 413extending from the linking rigid element 434 to a second rigid element433, and a fourth flexure 414 extending from the second rigid element433 to the carriage 441. The proximal end (not circled) of multiple-armlinkage 401 also includes corresponding flexures, the proximal end oflinking rigid element 434, and rigid elements that connect the base 431through the linking rigid element 434 to the carriage 441.

In the illustrated embodiment, multiple-arm linkages 401-404 areradially symmetric about the carriage motion line 42 or the carriage441, 90 degrees apart from each other. Each multiple-arm linkage,401-404, constrains motion of the carriage 441 along a plane parallel tothe orientation of the respective multiple arm linkage. Themotion-constrained planes 401 p, 402, 403 p, and 404 p, of multiple-armlinkages 401-404 intersect along a carriage-motion line, or a lineparallel to the carriage motion line 42. In FIG. 20A, the carriagemotion line 42 is parallel to the x-axis. Multiple-arm linkages 401-404,combined, constrain motion of the carriage 441 along the carriage motionline 42, or a line parallel to the carriage motion line 42.

FIG. 21A illustrates an isometric view of another four-arm, radiallysymmetric monolithic, linear-motion stage 410. Like linear-motion stage400, linear-motion stage 410 includes a base 431 and four multiple-armlinkages 401 a, 402 a, 403 a, and 404 a, radially spaced 90 degreesapart from each other around a carriage 441. Each multiple-arm linkage401 a-404 a constrains motion of the carriage 441 along a plane parallelto the orientation of the respective multiple-arm linkage. Themotion-constrained planes of multiple-arm linkages 401 a-404 a intersectalong a carriage-motion line 42, or a line parallel to the carriagemotion line 42.

Linear-motion stage 410 differs from linear-motion stage 400 byreplacing rigid elements and flexures extending between the base 431 andthe linking rigid elements 434 of each multiple-arm linkage 401 a-404 awith single blade flexures. For example, multiple-arm linkage 401 aincludes a blade flexure 411 a that extends from the base 431 to thelinking rigid element 434 and another blade flexure 412 a that extendsfrom the linking rigid element 434 to the carriage 441. The opposite endof multiple-arm linkage 401 a also includes corresponding blade flexuresand the opposite end of linking rigid element 434 that connect the base431 through the linking rigid element 434 to the carriage 441.

VIII. Other Linear Motion Stage Embodiments

In other embodiments, a linear-motion stage includes a base; a firstmultiple-arm linkage extends from the base to a first carriageattachment end; a second multiple-arm linkage extends from the firstcarriage attachment end to the base; a third multiple-arm linkageextends from the base to a second carriage attachment end; a carriageextends from the first carriage end to the second carriage end. Inembodiments, the first multiple-arm linkage constrains a motion of thecarriage to motion in a first plane and the second and thirdmultiple-arm linkages constrain the carriage to motion in a secondplane, the first and second planes intersect at a plane intersectionline. Additionally, the first, second, and third multiple-arm linkagesconstrain the motion of the carriage along a carriage motion line, thecarriage motion line is parallel to the plane intersection line. Also,the first, second, and third multiple-arm linkages comprise a first armrotateably connected to a second arm through a flexure, the angulartravel of the first arm is configured to be different than an angulartravel of the second arm as the carriage moves along the carriage motionline.

In other embodiments, at least one of the first, second, or thirdmultiple-arm linkages is homogeneously formed of a single material,having a joint-free continuity of the single material from a firstflexure, through a rigid element, to a second flexure. In still anotherembodiment, the first multiple-arm linkage comprises three firstmultiple-arm linkage flexures, the three first multiple-arm linkageflexures forming three corresponding first multiple-arm linkage rotationaxes that are substantially parallel to each other. Also, the secondmultiple-arm linkage comprises three, second multiple-arm linkageflexures, the three second multiple-arm linkage flexures forming threecorresponding second multiple-arm linkage rotation axes that aresubstantially parallel to each other and substantially orthogonal to thethree first multiple-arm linkage rotation axes. Likewise, the thirdmultiple-arm linkage comprises three third multiple-arm linkageflexures, the three third multiple-arm linkage flexures forming threecorresponding third multiple-arm linkage rotation axes that aresubstantially parallel to each other and the three, second multiple-armlinkage rotation axes.

In another embodiment, a linear-motion stage further comprises an opticsdevice attached to the carriage, the first carriage end, or the secondcarriage end, and the first, second, and third multiple-arm linkagesconstrain a motion of the optics device along the carriage motion line.In still other embodiments, each of the first, second, and thirdmultiple-arm linkages comprise a set of three flexures and two rigidelements, wherein each set of the three flexures and two rigid elementsare connected in series. Similarly, in other embodiments, the rigidelements have a rigid-element section moduli and the flexures have aflexure-section moduli, the rigid-element section moduli is orders ofmagnitude greater than the flexure-section moduli.

In another embodiment, a linear-motion stage further comprises a fourthmultiple-arm linkage extending from the second carriage end to the base,wherein the fourth multiple-arm linkage constrains the motion of thecarriage to motion in the first plane.

In another embodiment of the present disclosure, an apparatus comprisesa base; a first carriage end and a carriage extending from the firstcarriage end to a second carriage end; and first, second, and thirdmultiple arm linkages. The first multiple arm linkage comprises a firstflexure extending from the base to a first rigid element; a secondflexure extending from the first rigid element to a second rigidelement; and a third flexure extending from the second rigid element tothe first carriage end. The second multiple-arm linkage comprises afourth flexure extending from the first carriage end to a third rigidelement; a fifth flexure extending from the third rigid element to afourth rigid element; and a sixth flexure extending from the fourthrigid element to the base. A third multiple-arm linkage comprises aseventh flexure extending from the base to a fifth rigid element; aneighth flexure extending from the fifth rigid element to a sixth rigidelement; and a ninth flexure extending from a sixth rigid element to thesecond carriage end. In this embodiment, the first, second, and thirdflexures form a corresponding first, second, and third axis that aresubstantially parallel to each other. Similarly, the fourth, fifth, andsixth flexures form a corresponding fourth, fifth, and sixth axis thatare substantially parallel to each other and substantially orthogonal tothe first, second, and third axis. Finally, the seventh, eighth, andninth flexures form a corresponding seventh, eighth, and ninth axis thatare substantially parallel to each other and the fourth, fifth, andsixth axes.

In another embodiment of the present disclosure, a linear-motion stagecomprises a base; a first multiple-arm linkage extending from the baseto a carriage end; a second multiple-arm linkage extending from thecarriage end to the base; an optics device attached to the carriage end.In this embodiment, the first multiple-arm linkage constrains a motionof the optics device to motion in a first plane and the secondmultiple-arm linkage constrains the optics device to motion in a secondplane, the first and second planes intersecting at a plane intersectionline. Also, the first and second multiple-arm linkages constrain themotion of the optics device along a carriage motion line, the carriagemotion line being parallel to the plane intersection line. Similarly,the carriage attachment piece and the optics device are fully balancedsuch that a combined center of gravity of the carriage attachment pieceand the optics device is located in a balancing plane formed by a firstflexure extending from the first multiple-arm linkage to the carriageend and a second flexure extending from the carriage end to the secondmultiple-arm linkage.

In another embodiment, at least one of the first or second multiple-armlinkages is homogeneously formed of a single material, having ajoint-free continuity of the single material from a first flexure,through a rigid element, to a second flexure. In still anotherembodiment, the first multiple-arm linkage comprises three firstmultiple-arm linkage flexures, the three first multiple-arm linkageflexures forming three corresponding first multiple-arm linkage rotationaxes that are substantially parallel to each other. Similarly, thesecond multiple-arm linkage comprises three, second multiple-arm linkageflexures, the three, second multiple-arm linkage flexures forming threecorresponding second multiple-arm linkage rotation axes that aresubstantially parallel to each other and substantially orthogonal to thethree first multiple-arm linkage rotation axes.

In another embodiment, each of the first and second multiple-armlinkages comprise a set of three flexures and two rigid elements,wherein each set of the three flexures and two rigid elements areconnected in series. In another embodiment, each set of the threeflexures and the two rigid elements are connected in the followingorder: a first flexure, a first rigid element, a second flexure, asecond rigid element, and a third flexure. In another embodiment, therigid elements have a rigid-element section moduli and the flexures havea flexure-section moduli, the rigid-element section moduli being ordersof magnitude greater than the flexure-section moduli.

The foregoing description, for purposes of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the invention to the precise forms disclosed. Many modificationsand variations are possible in view of the above teachings. Theembodiments were chosen and described in order to best explain theprinciples of the present systems and methods and their practicalapplications, to thereby enable others skilled in the art to bestutilize the present systems and methods and various embodiments withvarious modifications as may be suited to the particular usecontemplated.

It will be appreciated that various of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also,various presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequentlymade by those skilled in the art, and are also intended to beencompassed by the following claims.

Unless otherwise noted, the terms “a” or “an,” as used in thespecification and claims, are to be construed as meaning “at least oneof” In addition, fore ease of use, the words “including” and “having,”as used in the specification and claims, are interchangeable with andhave the same meaning as the word “comprising.”

What is claimed is:
 1. A linear-motion stage comprising: a base; a firstmultiple-arm linkage extending from the base to a first carriageattachment piece; a second multiple-arm linkage extending from the firstcarriage attachment piece to the base; wherein: the first multiple-armlinkage constrains a motion of the first carriage attachment piece tomotion in a first plane and the second multiple-arm linkage constrainsthe first carriage attachment piece to motion in a second plane, thefirst and second planes intersecting at a plane intersection line; thefirst and second multiple-arm linkages constrain the motion of the firstcarriage attachment piece along a carriage motion line, the carriagemotion line being parallel to the plane intersection line; and the firstand second multiple-arm linkages are arranged angularly asymmetric withrespect to a plane transverse to the plane intersection line.
 2. Thelinear-motion stage of claim 1, wherein the first and secondmultiple-arm linkages are arranged radially asymmetric about thecarriage motion line.
 3. The linear-motion stage of claim 1, wherein thefirst carriage attachment piece is fully balanced such that a center ofgravity of the carriage attachment piece is located in a balancing planeformed by a first flexure extending from the first multiple-arm linkageto the first carriage piece and a second flexure extending from thefirst carriage piece to the second multiple-arm linkage.
 4. Thelinear-motion stage of claim 1, wherein the first multiple-arm linkageand the second multiple-arm linkage attach to the carriage attachmentpiece at an attachment plane, the attachment plane being orthogonal tothe plane intersection line.
 5. The linear-motion stage of claim 1,wherein at least a portion of one of the first or second multiple-armlinkages is homogeneously formed of a single material, having ajoint-free continuity of the single material from a first flexure to arigid element.
 6. The linear-motion stage of claim 5, wherein the rigidelement has a rigid-element section moduli and the flexure has aflexure-section moduli, the rigid-element section moduli being orders ofmagnitude greater than the flexure-section moduli.
 7. The linear-motionstage of claim 1, further comprising a third multiple-arm linkageextending from the base to a second carriage attachment piece.
 8. Thelinear-motion stage of claim 7, wherein: the third multiple-arm linkageconstrains a motion of the carriage to motion in a third plane; and thethird plane is parallel to the plane intersection line.
 9. Thelinear-motion stage of claim 7, further comprising a carriage extendingfrom the first carriage attachment piece to the second carriageattachment piece.
 10. The linear-motion stage of claim 7, furthercomprising a fourth multiple-arm linkage extending from the secondcarriage attachment piece to the base, wherein the fourth multiple-armlinkage constrains the motion of the carriage to motion in a fourthplane and the fourth plane is parallel to the plane intersection line.11. The linear-motion stage of claim 10, wherein the fourth plane isparallel to at least one of the first, second, or third planes.
 12. Thelinear-motion stage of claim 7, wherein: the first multiple-arm linkageattaches to the first carriage attachment piece at a first attachmentplane; the second multiple-arm linkage attaches to the first carriageattachment piece at a second attachment plane; the third multiple-armlinkage attaches to the second carriage attachment piece at a thirdattachment plane; and the fourth multiple-arm linkage attaches to thesecond carriage attachment piece at a fourth attachment plane.
 13. Amethod of moving a device comprising moving the device using thelinear-motion stage of claim
 1. 14. A linear-motion stage comprising: abase; a first carriage end and a carriage extending from the firstcarriage end to a second carriage end; and first, second, and thirdmultiple arm linkage sets, wherein: the first multiple arm linkage setcomprises a first flexure extending from the base to a first rigidelement; a second flexure extending from the first rigid element to asecond rigid element; and a third flexure extending from the secondrigid element to the first carriage end; the second multiple-arm linkagecomprises a fourth flexure extending from the first carriage end to athird rigid element; a fifth flexure extending from the third rigidelement to a fourth rigid element; and a sixth flexure extending fromthe fourth rigid element to the base; the third multiple-arm linkagecomprises a seventh flexure extending from the base to a fifth rigidelement; an eighth flexure extending from the fifth rigid element to asixth rigid element; and a ninth flexure extending from a sixth rigidelement to the second carriage end; the first, second, and thirdflexures form corresponding first, second, and third axis that aresubstantially parallel to each other; the fourth, fifth, and sixthflexures form a corresponding fourth, fifth, and sixth axis that aresubstantially parallel to each other and substantially orthogonal to thefirst, second, and third axis; and the seventh, eighth, and ninthflexures form a corresponding seventh, eighth, and ninth axis that aresubstantially parallel to each other and the fourth, fifth, and sixthaxes.
 15. A linear-motion stage, comprising: a base having a proximalbase end and a distal base end; a carriage having a proximal carriageend and a distal carriage end; and first, second, and third multiple-armlinkages, each multiple arm linkage comprising: a linking rigid element;a proximal attachment end that connects the proximal base end to theproximal carriage end through the linking rigid element; and a distalattachment end that attaches the distal base end to the distal carriageend through the linking rigid element; wherein: the first, second, andthird multiple-arm linkages constrain motion of the carriage torespective first, second, and third motion-constrained planes; thefirst, second, and third motion-constrained planes are parallel to acarriage-motion line; the first, second, and third multiple-arm linkagesconstrain motion of the carriage along the carriage-motion line; and atleast a portion of one of the first, second, or third multiple-armlinkages is homogeneously formed of a single material, having ajoint-free continuity of the single material from a flexure to a rigidelement.
 16. The linear-motion stage of claim 15, wherein the first,second, and third multiple-arm linkages are arranged radially symmetricabout the carriage motion line.
 17. The linear-motion stage of claim 15,further comprising a fourth multiple-arm linkage, the fourthmultiple-arm linkage comprising: a linking rigid element; a proximalattachment end that connects the proximal base end to the proximalcarriage end through the linking rigid element; and a distal attachmentend that attaches the distal base end to the distal carriage end throughthe linking rigid element; wherein: the fourth multiple-arm linkageconstrains motion to a fourth motion-constrained plane; the fourthmotion-constrained plane is parallel to the carriage-motion line; andthe fourth multiple-arm linkage constrains motion of the carriage alongthe carriage-motion line.
 18. The linear-motion stage of claim 17,wherein the first, second, third, and fourth multiple-arm linkages arearranged radially symmetric about the carriage motion line.
 19. Thelinear-motion stage of claim 15, wherein each multiple arm linkagefurther comprises: a first blade flexure extending from the proximalbase end to the proximal linking end; a second blade flexure extendingfrom the proximal linking end to the proximal carriage end; a thirdblade flexure extending from the distal base end to the distal linkingend; and a fourth blade flexure extending from the distal linking end tothe distal carriage end.
 20. A method of moving a device comprisingmoving a device using the linear-motion stage of claim 15.